Probabilistic optimal power flow considering the dependence of multiple wind farms using pair diffusive kernel copula

Abstract

As wind farms commonly gather in areas with abundant wind resources, spatial dependence of wind speeds among nearby wind farms should be taken into account when modeling a power system with large-scale wind power. In this paper, we first propose a novel bivariate non-parametric copula, bivariate diffusive kernel (BDK) copula, to formulate the dependence between random variables. Then, we extend the application of the BDK copula to high dimension by pair-copula method and name it as pair diffusive kernel (PDK) copula, which is flexible to formulate the complicated dependence structure of multiple random variables. Besides, a quasi-Monte Carlo (QMC) method, based on the combination of the Sobol sequence and the Rosenblatt transformation of the PDK copula, is elaborated in the sampling procedure to generate correlated wind speed samples. The proposed method is applied to solve the probabilistic optimal power flow (POPF) problems. We first validate the effectiveness of the BDK copula in copula definitions. Then, in order to verify the superior performance of the PDK copula in formulating the dependence structure of wind speeds among different wind farms, three different data sets are used in various goodness-of-fit (GOF) tests. Furthermore, samples obtained from the PDK copula are used to solve POPF problems, which are modeled on three modified IEEE 57-bus power systems. Compared with the Gaussian, T and parametric-pair copulas, the results obtained from the PDK copula are superior to formulate the complicated dependence in solving POPF problems.